Local regular dual reciprocity method for 2D convection-diffusion equation

Abstract

In this paper a new technique considering the dual reciprocity method (DRM) with only internal collocation points is considered along with local radial basis function interpolation. This approach gives rise to regular integral equations. Numerical results for the convection-diffusion equation are presented for different Peclet numbers. Comparisons with other numerical techniques are shown in order to illustrate the good solutions obtained by this method.

Time discretization versus state quantization in the simulation of a one-dimensional advection–diffusion–reaction equation

“…The ADR problem includes a wide range of configurations encompassing variable velocity fields, variable reaction coefficients, steady and transient problems, in one, two and three dimensions. 1–4…”

“…The ADR problem includes a wide range of configurations encompassing variable velocity fields, variable reaction coefficients, steady and transient problems, in one, two and three dimensions. [1][2][3][4] The ADR equation poses several challenges to numerical integration algorithms. First, as in most partial differential equations (PDEs), the space discretization usually leads to large systems of equations which require an efficient treatment.…”